Classical and Bayesian estimation for type-I extended-F family with an actuarial application

Nada M Alfaer; Sarah A Bandar; Omid Kharazmi; Hazem Al-Mofleh; Zubair Ahmad; Ahmed Z Afify

doi:10.1371/journal.pone.0275430

Classical and Bayesian estimation for type-I extended-F family with an actuarial application

PLoS One. 2023 Feb 2;18(2):e0275430. doi: 10.1371/journal.pone.0275430. eCollection 2023.

Authors

Nada M Alfaer¹, Sarah A Bandar², Omid Kharazmi³, Hazem Al-Mofleh⁴, Zubair Ahmad⁵, Ahmed Z Afify⁶

Affiliations

¹ Department of Mathematics & Statistics, College of Science, Taif University, Taif, Saudi Arabia.
² Department of Mathematics, College of Education, Misan University, Amarah, Iraq.
³ Department of Statistics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Pakistan.
⁴ Department of Mathematics, Tafila Technical University, Tafila, Jordan.
⁵ Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan.
⁶ Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt.

Abstract

In this work, a new flexible class, called the type-I extended-F family, is proposed. A special sub-model of the proposed class, called type-I extended-Weibull (TIEx-W) distribution, is explored in detail. Basic properties of the TIEx-W distribution are provided. The parameters of the TIEx-W distribution are obtained by eight classical methods of estimation. The performance of these estimators is explored using Monte Carlo simulation results for small and large samples. Besides, the Bayesian estimation of the model parameters under different loss functions for the real data set is also provided. The importance and flexibility of the TIEx-W model are illustrated by analyzing an insurance data. The real-life insurance data illustrates that the TIEx-W distribution provides better fit as compared to competing models such as Lindley-Weibull, exponentiated Weibull, Kumaraswamy-Weibull, α logarithmic transformed Weibull, and beta Weibull distributions, among others.

Copyright: © 2023 Alfaer et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Bayes Theorem
Computer Simulation
Likelihood Functions*
Monte Carlo Method
Statistical Distributions

Grants and funding

This study was funded by the Taif University Researchers Supporting 279 Project (TURSP-2020/316), Taif University, Taif, Saudi Arabia. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.